Deep neural network with dual-path bi-directional long short-term memory (BiLSTM) block has been proved to be very effective in sequence modeling, especially in speech separation, e.g. DPRNN-TasNet \cite{luo2019dual}. In this paper, we propose several improvements of dual-path BiLSTM based network for end-to-end approach to monaural speech separation. Firstly a dual-path network with intra-parallel BiLSTM and inter-parallel BiLSTM components is introduced to reduce performance sub-variances among different branches. Secondly, we propose to use global context aware inter-intra cross-parallel BiLSTM to further perceive the global contextual information. Finally, a spiral multi-stage dual-path BiLSTM is proposed to iteratively refine the separation results of the previous stages. All these networks take the mixed utterance of two speakers and map it to two separate utterances, where each utterance contains only one speaker's voice. For the objective, we propose to train the network by directly optimizing the utterance level scale-invariant signal-to-distortion ratio (SI-SDR) in a permutation invariant training (PIT) style. Our experiments on the public WSJ0-2mix data corpus results in 20.55dB SDR improvement, 20.35dB SI-SDR improvement, 3.69 of PESQ, and 94.86\% of ESTOI, which shows our proposed networks can lead to performance improvement on the speaker separation task. We have open-sourced our re-implementation of the DPRNN-TasNet in https://github.com/ShiZiqiang/dual-path-RNNs-DPRNNs-based-speech-separation, and our LaFurca is realized based on this implementation of DPRNN-TasNet, it is believed that the results in this paper can be reproduced with ease.